MathDB

Let

A=\{1,3,3^2,\ldots, 3^{2014}\}

. We obtain a partition of

A

A

is written as a disjoint union of nonempty subsets.
[*]Prove that there is no partition of

A

such that the product of elements in each subset is a square. [*]Prove that there exists a partition of

A

such that the sum of elements in each subset is a square.

Problem Statement